Mathematical Notes

, Volume 59, Issue 5, pp 463–476 | Cite as

Partially decomposable and totally indecomposable nonnegative matrices

  • Y. V. Bolotnikov
  • V. E. Tarakanov


We considerm×n (m≤n) matrices with entries from an arbitrary given finite set of nonnegative real numbers, including zero. In particular, (0, 1)-matrices are studied. On the basis of the classification of such matrices by type and of the general formula for the number of matrices of nullityt valid fort>n andt≥n>m (see [2]), an asymptotic (asn → ∞) expansion is obtained for the total number of: (a) totally indecomposable matrices (Theorems 1 and 5), (b) partially decomposable matrices of given nullityt≥n (Theorems 2 and 4), (c) matrices with zero permanent (without using the inclusion-exclusion principle; Corollary of Theorem 2).


Real Number General Formula Nonnegative Real Number Nonnegative Matrice Decomposable Matrice 
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    V. N. Sachkov,Probabilistic Methods in Combinatorial Analysis [in Russian], Nauka, Moscow (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Y. V. Bolotnikov
    • 1
  • V. E. Tarakanov
    • 1
  1. 1.Steklov Mathematics InstituteRussian Academy of SciencesUSSR

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